Weakened but still potent, Barry has inundated the Gulf Coast but appeared unlikely to deluge New Orleans as it continued its slow advance.
Still, Louisiana Governor John Bel Edwards on Saturday night urged residents across south Louisiana to stay "vigilant", warning that Barry could still cause disastrous flooding across a wide stretch of the Gulf Coast overnight.
"This storm still has a long way to go before it leaves this state," Edwards said. "Don't let your guard down."
New Orleans had been braced for heavy rains Saturday, but instead had intermittent bands of moderate showers and occasional sunshine.
Though Barry will continue to dump rain throughout the weekend, forecasters downgraded rainfall estimates for the city through Sunday to between 5 and 10 centimetres.
Forecasters had earlier said New Orleans could get up to 50cm of rain, raising concerns that water pumps strengthened after Hurricane Katrina would be overwhelmed.
National Weather Service forecaster Robert Ricks cautioned, however, that it was too early to say for certain that New Orleans was in the clear.
"We're about at the (halfway) mark of the marathon right now," he said Saturday evening.
Heavy rainfall from the storm would be concentrated overnight in a wide area centred around Lafayette, he said.
The city is about 193km west of New Orleans.
Late Saturday night, authorities were trying to rescue a family of five who was trapped by high water in the south Louisiana town of Franklin, according to KTBS-TV.
The National Guard had to halt its initial rescue mission because waters were too high to safely reach the family's home. Franklin is about 64km southeast of Lafayette.
In other parts of Louisiana on Saturday, Barry flooded highways, forced people to scramble to rooftops and dumped heavy rain, as it made landfall near Intracoastal City, about 257km west of New Orleans.
Downpours also lashed coastal Alabama and Mississippi.
After briefly becoming a Category 1 hurricane, the system weakened to a tropical storm, the National Hurricane Center said.
By late Saturday night, its maximum sustained winds had fallen to 80km/h.
Coast Guard helicopters rescued a dozen people and two pets from flooded areas of Terrebonne Parish, south of New Orleans, some of them from rooftops, a spokeswoman said.
Those rescued included a 77-year-old man who called for help because he had about 1.2 meters of water in his home.